Problem: Divide the following complex numbers. $ \dfrac{-20+4i}{4i}$
Answer: Since we're dividing by a single term, we can simply divide each term in the numerator separately. $ \dfrac{-20+4i}{4i} = \dfrac{-20}{4i} + \dfrac{4i}{4i}$ Factor out a $1/i$ $\dfrac{-20}{4i} + \dfrac{4i}{4i} = \dfrac 1i \left( \dfrac{-20}{4} + \dfrac{4i}{4} \right) = \dfrac 1i (-5+i)$ After simplification, $1/i$ is equal to $-i$, so we have: $\dfrac 1i (-5+i) = -i (-5+i) = 5i - 1i^2 = 1+5i$